To each self-conjugate spin\(^c\)  structure \(\mathfrak {s}\) , i.e. \(\mathfrak {s}=\bar{\mathfrak {s}}\) , on a closed oriented three-manifold \(Y\)  we associate in [1]} the \(\mathrm {Pin}(2)\) -monopole Floer homology groups, which fit in the long exact sequence
\(\cdots \stackrel{i_*}{\longrightarrow }\widehat{\mathit {HS}}\) 
